As an image scaling (enlarging or reducing) method, a nearest neighbor method, and the like, is known. In case of the nearest neighbor method, when an image formed of pixels, being arranged in two dimensions, which are the main scanning direction and sub-scanning direction as shown in FIGS. 18a, 18b and 18c as an example, are to be enlarged in the sub-scanning direction, pixels are copied in a pixel insertion cycle according to the enlargement ratio, and the copied pixels are inserted below the pixels in the sub-scanning direction. FIG. 18a illustrates the pixel insertion cycle, FIG. 18b illustrates an original image, and FIG. 18c illustrates the image after scaling (enlarging). The original image, illustrated in FIG. 18b, is an image in which a pattern of “two white lines between a black line and a black line” repeats. In case of the image after scaling, as illustrated in FIG. 18c, a white line is copied at the position of pixel insertion cycle and the copied white line is inserted below the white line, and therefore, the areas where three white lines exist between a black line and a black line are produced.
Although image sharpness can be maintained in cases of scaling by using the nearest neighbor method, or the like, density unevenness occurs in the image in the form of horizontal streaks in cases of an image of a fine pattern because the position of insertion of pixel is lined on the same line.
Meanwhile, an image scaling method, in which the pixel inserting position is dispersed, has been disclosed. FIGS. 19a, 19b, and 19c illustrate examples of cases in which the pixel inserting position is dispersed in accordance with a repeating pattern of a V character. FIG. 19a illustrates a dispersal pattern, FIG. 19b illustrates an original image, and FIG. 19c illustrates a scaled image in which pixels have been inserted in accordance with the dispersal pattern of FIG. 19a. In case of the above-mentioned dispersing method, because the position of insertion of pixels is dispersed, density unevenness becomes less noticeable when compared with the image after scaling illustrated in FIG. 18c. 
However, the local density varies at the pixel inserting position. As an example, as illustrated in FIGS. 20a and 20b, when compared with the original image (FIG. 20a) in which two black lines and three white lines appear periodically, in the case of the scaled image (FIG. 20b) which has been formed by inserting white pixel P1 and black pixel P2 in the original image, the local density decreases near the position where white pixel P1 has been inserted, while on the other hand, the local density increases near the position where black pixel P2 has been inserted. In cases of deleting pixels for image scaling (reducing), the local density increases near the position where a white pixel has been deleted, and the local density decreases near the position where a black pixel has been deleted.
In order to overcome this problem, methods to determine the density of inserted pixels have been suggested so that density in the vicinity of the pixel inserting position before and after pixel insertion remains constant.
As an example, an image enlargement/reduction apparatus has been disclosed in Unexamined Japanese Patent Application Publication No. 1987-213383 (hereinafter referred to as Patent Document 1), in which, in a case of representing a pseudo-halftone by using white pixels and black pixels, a part of the pixels, in the vicinity of the position where a pixel has been inserted or deleted, is replaced by white or black pixels so that the density near inserted or deleted pixel does not change before and after pixel insertion or deletion.
Also, in Unexamined Japanese Patent Application Publication No. 2006-80712 (hereinafter referred to as Patent Document 2), a technology has been disclosed in which, when an error diffusion process, in which density error, which occurs when a target pixel of a multilevel is binarized, is distributed to pixels in the vicinity thereof, and registration correction to correct pixel position deviation is performed, if a target pixel in the error diffusion process is the pixel located in the position where density is to be corrected during registration correction, the density value of the target pixel is distributed to peripheral pixels as an error with no change.
When adapting a method in which the density of inserted pixel is determined so that the density of the vicinity of the pixel inserting position before and after pixel insertion remains constant, there will be no problem if the density of the pixel of the pixel inserting position is adjusted or density error is distributed to peripheral pixels by using an error diffusion process, or the like, concurrently as described in the above-mentioned Patent Documents 1 and 2. However, in cases in which an error diffusion process is not used concurrently, isolated points are generated at pixel inserting positions, resulting in a change of the image form before and after pixel insertion.
As an example, as illustrated in FIGS. 21a, 21b, and 21c, in a case of a simple method in which the pixel value of inserted pixel is adjusted (in this example, pixel value is adjusted to 128) so as to maintain the average density of the vicinity of the pixel inserting position before and after pixel insertion by obtaining the average density of the vicinity of the pixel inserting position before pixel insertion (FIG. 21a), and the average density of the vicinity of the pixel inserting position after white pixel P1 is inserted in the pixel inserting position (FIG. 21b), the inserted pixel becomes an intermediate density value at isolated point P1′, resulting in a change of the image form when compared with the original image.